%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN008-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n028.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 29 23:53:08 EDT 2022

% Result   : Unsatisfiable 0.19s 0.37s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   22 (   4 unt;   3 typ;   0 def)
%            Number of atoms       :   58 (   0 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :   57 (  18   ~;  26   |;   0   &)
%                                         (  13 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    0 (   0 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   5 prp; 0-0 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :    0 (   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(r_type,type,
    r: $o ).

tff(q_type,type,
    q: $o ).

tff(p_type,type,
    p: $o ).

tff(1,plain,
    ( ( $false
      | $false
      | $false )
  <=> $false ),
    inference(rewrite,[status(thm)],]) ).

tff(2,plain,
    ( ~ $true
  <=> $false ),
    inference(rewrite,[status(thm)],]) ).

tff(3,axiom,
    r,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).

tff(4,plain,
    ( r
  <=> $true ),
    inference(iff_true,[status(thm)],[3]) ).

tff(5,plain,
    ( ~ r
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[4]) ).

tff(6,plain,
    ( ~ r
  <=> $false ),
    inference(transitivity,[status(thm)],[5,2]) ).

tff(7,axiom,
    ~ q,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).

tff(8,plain,
    ( q
  <=> $false ),
    inference(iff_false,[status(thm)],[7]) ).

tff(9,axiom,
    ~ p,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).

tff(10,plain,
    ( p
  <=> $false ),
    inference(iff_false,[status(thm)],[9]) ).

tff(11,plain,
    ( ( p
      | q
      | ~ r )
  <=> ( $false
      | $false
      | $false ) ),
    inference(monotonicity,[status(thm)],[10,8,6]) ).

tff(12,plain,
    ( ( p
      | q
      | ~ r )
  <=> $false ),
    inference(transitivity,[status(thm)],[11,1]) ).

tff(13,plain,
    ( ( p
      | ~ r
      | q )
  <=> ( p
      | q
      | ~ r ) ),
    inference(rewrite,[status(thm)],]) ).

tff(14,plain,
    ( ( ~ r
      | p )
  <=> ( p
      | ~ r ) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,plain,
    ( ( ~ r
      | p
      | q )
  <=> ( p
      | ~ r
      | q ) ),
    inference(monotonicity,[status(thm)],[14]) ).

tff(16,plain,
    ( ( ~ r
      | p
      | q )
  <=> ( p
      | q
      | ~ r ) ),
    inference(transitivity,[status(thm)],[15,13]) ).

tff(17,axiom,
    ( ~ r
    | p
    | q ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).

tff(18,plain,
    ( p
    | q
    | ~ r ),
    inference(modus_ponens,[status(thm)],[17,16]) ).

tff(19,plain,
    $false,
    inference(modus_ponens,[status(thm)],[18,12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SYN008-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n028.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Mon Sep  5 01:07:55 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34  Usage: tptp [options] [-file:]file
% 0.12/0.34    -h, -?       prints this message.
% 0.12/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.34    -m, -model   generate model.
% 0.12/0.34    -p, -proof   generate proof.
% 0.12/0.34    -c, -core    generate unsat core of named formulas.
% 0.12/0.34    -st, -statistics display statistics.
% 0.12/0.34    -t:timeout   set timeout (in second).
% 0.12/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34    -<param>:<value> configuration parameter and value.
% 0.12/0.34    -o:<output-file> file to place output in.
% 0.19/0.37  % SZS status Unsatisfiable
% 0.19/0.37  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------